Brief Information

• Name : Vector Calculus and Exercises
• Lecturer : 강영옥
• Semester : 2014 Winter
• Course :?Liberal arts
• Textbook
  1. 송영권, 송형수, 이종우, 이흥수, 지은숙, 허민 (2009) 벡터해석. 교우사
  2. Thomas, G., B. (2006) 미분적분학. 11 Ed. 자유아카데미
• Syllabus 😕Syllabus__Vector Calculus and Exercises
• In?short
  • This lecture focused on understanding vector calculus by intuition rather than?by?strict?mathematical proof.
  • Vector calculus?:? a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space

Supplements for self-study

• Murray R. Spiegel, Seymour Lipschutz, and Denis Spellman. (2009) Vector Analysis. McGraw-Hill

Trace lectures

• 3 coordinate systems: rectangular/cylindrical/spherical coordinate system
• scalar and vector
• vector space
• projection
• dot product, cross product
• triple product
• equation of lines
• equation of planes
• vector function
• limit of vector functions
• continuity of vector functions
• curve
• position vector X
• parametric curve
• tangent vectors of a curve, an unit tangent vectors?T
• length of a curve
• parametric equation by length parameter
• curvature $latex kappa $
• radius of curvature, circle of curvature
• principal unit normal vector?N
• unit binormal vector B
• function of several variables, multivariate function
• level curve, level surface
• limit?of multivariate functions
• continuity of multivariate functions
• partial differentiation of multivariate functions, partial derivative, second order partial derivative
• ordinary differentiation?of multivariate functions
• tangent plane
• linear approximation, true value, approximate value, error, absolute error, relative error, percentage error
• chain rule when?differentiation of?multivariate functions
• differentiation of implicit functions
• gradient of?multivariate functions
• directional derivative of?multivariate functions?on a directional vector
• tangent plane described by gradient, normal line described by gradient
• extremums?of?multivariate functions, extreme point
• maximum, maximal point, minimum, minimal point
• critical point
• saddle point
• determinant of a?critical point if an?extremum (?)
• double integral, iterated integral
• Fubini’s Theorem
• double integral on polar coordinate
• midterm exam
• final exam

Assignments

1. Solve Exercises?1.1 ~ 3.3 (2014-12-26~27)
   [1.1] 2-3, 3-5, 6-2, 6-5, 7-2, 8-2
   [1.2] 4, 5, 6
   [1.3] 3, 5, 8, 9
   [2.1] 1-1, 1-3, 5-2, 7
   [2.2] 2, 3, 6, 13-3, 13-6
   [3.2] 2, 3-4, 5
   [3.3] 2, 6, 10
2. Solve Exercises 3.4 ~ 4.1 (2014-12-28~2015-01-02)
   [3.4] 2, 3-2, 5, 8
   [3.5] 1-2, 1-3, 3-2, 5
   [3.6] 2-4, 8, 10
   [3.7] 1-3, 1-5
   [4.1] 2-5, 2-6, 2-7, 3-2, 3-3, 3-4, 4-2, 6, 8, 10-2, 10-3

Summarize?themes

• position vector, velocity, acceleration